The game :Veptheca is an abstract
strategy game for two or more players,
which is played with pen and paper or other surface (blackboard,
indigo-board or even sand). The name of the game means Vector (int.)
and Eptheca (addition, lat.). The main game rules are related to
"connected vector", "vector" and "vector addition" in math.

Vector addition :

Very important knowledge for playing Veptheca is a rule for vector
addition. The sum of vectors A and B is the vector C, which can be
calculated with the following rule :

Game rules :

The board of Veptheca is a square array of dots. The minimal
size is 3x3 points, but bigger is better, for more strategy (I
reccomend at least 4x4). Of course,
for more than two players, bigger field must be used.

empty minimal playing-field 3X3.

Every player draws a vector on the
field, with the following rules :

1. Horizontal or vertical vector, with length 1 (the distance, between
two neighbour
dots, in same line or column) with arbitrary direction, if the vector
doesn't intersect any existing one.
OR
2. Vector, whose is a sum of two existing connected vectors (non marked
*), with joint
vertex, if :

is a "discreet" (i.e. is drawn from dot to dot);

doesn't intersect existing vector;

must be joint with both vectors, whose sum is it (all 3 vectors
must be joint, each to each);

for preventing multiple usage of already used vectors, mark the
vectors, whose sum is it *.

The winner of the game, is the player, who makes the last possible move.
* This is a rule of multiple usage. The players can choose to play with
or without it. I reccomend to play with this rule.

Examples of valid
moves :
The game may look i little complex, but actually the rules are very
simple. Here are some examples of VALID
moves :

correct sum of two vectors

another correct sum of two vectors

one more correct vector - sum of two orthogonal vectors

This is a legal move with the latest game rules.

the longest blue vector is a sum of the two red vectors

Examples of invalid moves :
Here are some samples of INVALID moves
in the game - the GREEN vector
shows the invalid move :

the green vector intersects the existing blue vector.

the green vector is a sum of the blue and red vector, but only in math.
In Veptheca, source vectors must have joint vertex.

another incorrect move in Veptheca - the sum vector doesn't have joint
vertex with the first vector.

Game example :

These are animations, which shows a sample games on a minimal
playing-field (3X3) for two players. The moves are in different colors
just for clarity. The red player begins the game :